Analysis of Radiative Equilibrium in a Rectangular Enclosure With Gray Medium

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Abstract
Radiative heat transfer and temperature profile in a two-dimensional rectangular enclosure with gray medium are calculated. Successive approximate solutions are generated by a point allocation method in which the temperature profile is expressed as polynomials of successively higher order. The technique is shown to converge rapidly with the third-order results already comparing favorably with available numerical solution. It is also demonstrated to be computationally efficient. Comparing with a solution with the same number of unknowns generated by the Hottel zonal method, the present approach represents a reduction in computational time by at least one order of magnitude. Based on the mathematical behavior of the numerical results, simple empirical closed-form approximate expressions for both the heat transfer and temperature profile in general multidimensional systems at radiative equilibrium are proposed. For a rectangular enclosure, these expressions are demonstrated to be quite accurate over all optical thickness.

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